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QR matrix decomposition

Posted: 20 Jan 2009 ?? ?Print Version ?Bookmark and Share

Keywords:matrix decomposition QR? MIMO? OFDM?

QR matrix decomposition (QRD), sometimes referred to as orthogonal matrix triangularization, is the decomposition of a matrix (A) into an orthogonal matrix (Q) and an upper triangular matrix (R). QRD is useful for solving least squares' problems and simultaneous equations.

In wireless applications, there are prevalent cases where QRD is useful. Multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems often require small multiple matrix (for example, 4 x 4) inversions. These systems typically use a non-recursive technique, such as QRD. Digital predistortion (DPD) and joint detection applications often require large single matrix (for example, 20 x 20) inversions. DPD often also requires a recursive technique, such as the QRD recursive least squares (QRD-RLS) algorithm, because the equations are overspecified matrix A has more rows than there are unknowns (N) to calculate.

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